scholarly journals Perturbation bounds for the metric projection of a point onto a linear manifold in reflexive strictly convex Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (19) ◽  
pp. 6829-6836
Author(s):  
Jianbing Cao ◽  
Hongwei Jiao
Keyword(s):  
Banach Spaces ◽  
Generalized Inverse ◽  
Linear Manifold ◽  
Metric Projection ◽  
Operator Equations ◽  
Perturbation Bounds ◽  
Strictly Convex ◽  
Ill Posed ◽  
Strictly Convex Banach Spaces ◽  
Metric Generalized Inverse

In this paper, by using some recent perturbation bounds for the Moore-Penrose metric generalized inverse, we present some results on the perturbation analysis for projecting a point onto a linear manifold in reflexive strictly convex Banach spaces. The main results have two parts, part one covers consistent operator equations and part two covers the general so-called ill posed operator equations.

scholarly journals Metric Projection Operator and Continuity of the Set-Valued Metric Generalized Inverse in Banach Spaces

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Shaoqiang Shang ◽  
Jingxin Zhang
Keyword(s):  
Banach Spaces ◽  
Projection Operator ◽  
Generalized Inverse ◽  
Metric Projection ◽  
Generalized Inverses ◽  
Strictly Convex ◽  
Metric Generalized Inverse ◽  
Convex Spaces

In this paper, continuous homogeneous selection and continuity for the set-valued metric generalized inverses T∂ in 3-strictly convex spaces are investigated by continuity of metric projection. The results are an answer to the problem posed by Nashed and Votruba. Moreover, authors prove that there exists a proximinal hyperplane H such that PH is continuous and H is not approximative compact.

Perturbation bounds for the Moore–Penrose metric generalized inverse in some Banach spaces

2018 ◽  
Vol 9 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Jianbing Cao ◽  
Wanqin Zhang
Keyword(s):  
Banach Spaces ◽  
Generalized Inverse ◽  
Perturbation Bounds ◽  
Metric Generalized Inverse

scholarly journals Minimal periods for ordinary differential equations in strictly convex Banach spaces and explicit bounds for someLp-spaces

2014 ◽  
Vol 256 (8) ◽  
pp. 2846-2857 ◽  
Author(s):  
Michaela A.C. Nieuwenhuis ◽  
James C. Robinson ◽  
Stefan Steinerberger
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Banach Spaces ◽  
Strictly Convex ◽  
Explicit Bounds ◽  
Strictly Convex Banach Spaces

MAZUR–ULAM PROPERTY OF THE SUM OF TWO STRICTLY CONVEX BANACH SPACES

2015 ◽  
Vol 93 (3) ◽  
pp. 473-485 ◽  
Author(s):  
JIAN-ZE LI
Keyword(s):  
Banach Spaces ◽  
Equivalent Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Extension Problem ◽  
Isometric Extension ◽  
Strictly Convex ◽  
Necessary And Sufficient ◽  
Strictly Convex Banach Spaces ◽  
Equivalent Conditions

In this article, we study the Mazur–Ulam property of the sum of two strictly convex Banach spaces. We give an equivalent form of the isometric extension problem and two equivalent conditions to decide whether all strictly convex Banach spaces admit the Mazur–Ulam property. We also find necessary and sufficient conditions under which the $\ell ^{1}$-sum and the $\ell ^{\infty }$-sum of two strictly convex Banach spaces admit the Mazur–Ulam property.

Approximate best proximity point sequences for C*λ mappings in strictly convex Banach spaces

2019 ◽  
Vol 43 (12) ◽  
pp. 1791-1807
Author(s):  
M. Gabeleh ◽  
S.P. Moshokoa ◽  
O. Olela Otafudu
Keyword(s):  
Banach Spaces ◽  
Best Proximity Point ◽  
Strictly Convex ◽  
Strictly Convex Banach Spaces

NONEXPANSIVE BIJECTIONS TO THE UNIT BALL OF THE -SUM OF STRICTLY CONVEX BANACH SPACES

2018 ◽  
Vol 97 (2) ◽  
pp. 285-292 ◽  
Author(s):  
V. KADETS ◽  
O. ZAVARZINA
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Convex Banach Space ◽  
Strictly Convex ◽  
Strictly Convex Banach Space ◽  
Strictly Convex Banach Spaces

Extending recent results by Cascales et al. [‘Plasticity of the unit ball of a strictly convex Banach space’, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat.110(2) (2016), 723–727], we demonstrate that for every Banach space $X$ and every collection $Z_{i},i\in I$, of strictly convex Banach spaces, every nonexpansive bijection from the unit ball of $X$ to the unit ball of the sum of $Z_{i}$ by $\ell _{1}$ is an isometry.

scholarly journals Convergence of Ishikawa iterates of generalized nonexpansive mappings

1997 ◽  
Vol 20 (3) ◽  
pp. 517-520 ◽  
Author(s):  
M. K. Ghosh ◽  
L. Debnath
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Strictly Convex ◽  
Strictly Convex Banach Spaces

This paper is concerned with the convergence of Ishikawa iterates of generalized nonexpansive mappings in both uniformly convex and strictly convex Banach spaces. Several fixed point theorems are discussed.

scholarly journals Strong and weak convergence of Ishikawa iterations for best proximity pairs

2020 ◽  
Vol 18 (1) ◽  
pp. 10-21
Author(s):  
Moosa Gabeleh ◽  
S. I. Ezhil Manna ◽  
A. Anthony Eldred ◽  
Olivier Olela Otafudu
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Relatively Nonexpansive Mapping ◽  
Strictly Convex ◽  
Strong And Weak Convergence ◽  
Uniformly Convex Banach Spaces ◽  
Relatively Nonexpansive ◽  
Strictly Convex Banach Spaces ◽  
Best Proximity Pair

Abstract Let A and B be nonempty subsets of a normed linear space X. A mapping T : A ∪ B → A ∪ B is said to be a noncyclic relatively nonexpansive mapping if T(A) ⊆ A, T(B) ⊆ B and ∥Tx − Ty∥ ≤ ∥x − y∥ for all (x, y) ∈ A × B. A best proximity pair for such a mapping T is a point (p, q) ∈ A × B such that p = Tp, q = Tq and d(p, q) = dist(A, B). In this work, we introduce a geometric notion of proximal Opiaľs condition on a nonempty, closed and convex pair of subsets of strictly convex Banach spaces. By using this geometric notion, we study the strong and weak convergence of the Ishikawa iterative scheme for noncyclic relatively nonexpansive mappings in uniformly convex Banach spaces. We also establish a best proximity pair theorem for noncyclic contraction type mappings in the setting of strictly convex Banach spaces.

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